Electronic Circular Dichroism of Transition Metal Complexes within TDDFT Jing Fan University of Calgary 1
Jan 29, 2016
Electronic Circular Dichroism of Transition Metal Complexes
within TDDFTJing Fan
University of Calgary
1
Objectives To understand, experimental CD spectra, quantum
mechanical calculations of electronic structure and CD based on TDDFT
To elucidate the origin of CD in typical transition metal complexes, relationship between CD and molecular geometry
To evaluate the reliability and accuracy of TDDFT for transition metal compounds
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Complexes Studied:Trigonal Dihedral:
− both - and π-bonded complexes: [M(L-L)3]n+ (M = Co, Cr; L =
ox, acac, thiox, etc.)(d-to-d, LMCT, MLCT, LC)
− complexes with conjugated ligands: [M(L-L)3]2+ ( M = Fe, Ru, Os; L = bpy, phen)(LC exciton CD )
Trigonal bipyramidal: − complexes with conjugated ligands [M(L)X]+ (M = Cu, Zn; L = MeTPA, MeBQPA, MeTQA; X = Cl-, NCS-)(LC exciton CD)
− -bonded complexes: [M(en)3]3+ (M = Co, Cr) (d-to-d, LMCT)
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Computational Details ADF package Basis sets (STO): • ligand atoms: frozen core triple- polarized “TZP” -C, N, O (1S); S (2p) • metal atoms: -Co, Cr : TZP (2p); -Fe, Ru, Os: TZ2P (2p, 3d, 4f) Functionals: VWN (LDA) + BP86 (GGA) Relativistic effect for Fe group metals (scalar ZORA) Un-restricted calculations for Cr(III) The “COnductor-like continuum Solvent MOdel” (COSMO) of solvation
-bonded Complexes : [Co(en)3]3+ and [Cr(en)3]3+
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H2N NH2
en:d-d LMCT
• Calculated E are systematically overestimated for the d-d region (by ~5,500 cm-1); underestimated for the LMCT region (by ~6,000 cm-1)
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Lowest singlet excited states and their splitting in D3 symmetry
Assignment of Transitions
(1A2)
(2E)
(3E)
(2A2)
(1E)
Λ-[Co(en)3]3+
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Why Optically Active?
1A1g 1T1g d-d transitions: magnetically allowed1A1g 1T1u LMCT transitions: electrically allowed
electric transition dipole moment
magnetic transition dipole moment
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R0λ = Im 0 ˆ Θ λ ⋅ λ ˆ M 0
Rotatory Strengths:
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Metal d-orbitals:
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eg:1(− 1/3dx2−y2 + 2/3dyz)
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eg:2( 1/3dxy − 2/3dxz)
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t2g:1(dz2 )
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t2g:2( 2/3dx2−y2 + 1/3dyz)
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t2g:3(− 2/3dxy − 1/3dxz)
dσ1 dσ2
dπ2dπ1 dπ3
L-orbitals:
Symmetry Metal and Ligand Frontier Orbitals
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• Metal-ligand orbital interactions
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a1σ
€
a2σ
€
1ˆ e xσ
€
1ˆ e yσ
€
2ˆ e xσ
€
2ˆ e yσ
CH2H2C
H2N NH2
CH2H2C
H2N NH2
Origin of Optical Activity
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In general
,
,
,
,
ExpressionOverlaps
S(d1,1ex )
S(d2 ,1ey )
S(d1,2ex )
S(d2 ,2ey )
S(d1,a1 )
S(d 2 ,1ex )
S(d 3 ,1ey )
S(d 2 ,2ex )
S(d 3 ,2ey )
€
b
2a
1
2(b2 − a2 sin2 ω
b2 ) + (a2 sin2ω
b2 ) ⎡
⎣ ⎢
⎤
⎦ ⎥Sσ '
€
(1
2sinω + cosω)Sσ '
3 3
2(
a2 cos2a2 b2
1
3)S
€
−b
2a(b2 − a2 sin2 ω
b2) −
1
2(a2 sin2ω
b2)
⎡
⎣ ⎢
⎤
⎦ ⎥Sσ '
€
−(sinω −1
2cosω)Sσ '
Semi-quantitative Metal-ligand Orbital Overlaps
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Sσ ' =3ab
a2 + b2Sσ
b
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aM
N
N
N
N
N
N
-0.160 S-0.021 S0,
-0.102 S0.096 S0,
0.287 S0.047 S0
0.013 S-0.001 S0,
1.193 S1.220 S1.225 S,
Case IIICase II Case IOverlaps
S(d1,a1 )
)ˆ2,( 1 xedS )ˆ2,( 2
yedS
)ˆ1,( 2 yedS)ˆ1,( 1
xedS
)ˆ1,( 2 xedS )ˆ1,( 3
yedS
)ˆ2,( 2 xedS )ˆ2,( 3
yedS
Case I: Oh, = 60Case II: D3, = −6.3 Case III: D3, = +6.3-[Co(en)3]3+
1 e ( 3 /2)1e (1/2)2e ,2 e (1/2)1e ( 3 /2)2e
1010
Ene
rgy
(eV
)
MO diagram
MOs as linear combinations of symmetry ligand and metal d-orbitals
na2c(na2)a2
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na1= c(na1,i)
i
2
∑ χ i
nex,y c(nex,y,i)
i
4
i
(1 a1 ,2 d1)
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(χ 1 =1ˆ e σ ,χ 2 = 2ˆ e σ ,χ 3 = dσ ,χ 4 = dπ )
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3e = 0.88661ˆ e σ + 0.1176dπ
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4 e = −0.09791ˆ e σ + 0.9725dπ
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5e = 0.8582dσ − 0.77882ˆ e σ
Main components from DFT calculations
bonding
anti-bonding
anti-bonding
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and in terms of one-electron excitations 4e(d) 5e(d)€
R 1A21
( ) = Im A11 ˆ μ 1A2
1 ⋅ 1A21 ˆ m A1
1[ ]
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R 1A21
( ) =4 2
3c(4ex,1)c(5ey,2) 1ˆ e xσ z 2ˆ e yσ[ ] ⋅ c(5ey,3)c(4ex,4) ⋅ dxy mz dx 2 −y 2 − dxz mz dyz( )[ ]
• Prediction of the Sign of Rotatory Strengths
Band 2:
A11 1A2
1
z
y
x
1 e x
2 e y
positive
negative
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Metal d-orbitals:
€
eg:1(− 1/3dx2−y2 + 2/3dyz)
€
eg:2( 1/3dxy − 2/3dxz)
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t2g:1(dz2 )
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t2g:2( 2/3dx2−y2 + 1/3dyz)
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t2g:3(− 2/3dxy − 1/3dxz)
dσ1 dσ2
dπ2dπ1 dπ3
L-orbitals:
L-orbitals:
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a1
€
a2
€
1ex
€
1ey
€
2ex
€
2ey
€
a1
€
a2
€
1ex
€
1ey
€
2ey
€
2ex
Metal and Ligand Frontier Orbitals
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Both - and π-bonded Complexes
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overlap* overlap
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S dσ 1,1exσ
( );S dσ 2 ,1eyσ
( )
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S dσ 1,2exσ
( );S dσ 2 ,2eyσ
( )
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S dπ1,a1σ
( )
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S dπ 2 ,1exσ
( );S dπ 3 ,1eyσ
( )
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S dπ 2 ,2exσ
( );S dπ 3 ,2eyσ
( )
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b
2a
1
2
b2 − a2 sin2 ω
b2
⎛
⎝ ⎜
⎞
⎠ ⎟+
a2 sin2ω
b2
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥Sσ '
€
1
2sinω + cosω
⎛
⎝ ⎜
⎞
⎠ ⎟Sσ '
€
−3 3
2
a2 cos2ω
a2 + b2−
1
3
⎛
⎝ ⎜
⎞
⎠ ⎟Sσ
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−b
2a
b2 − a2 sin2 ω
b2
⎛
⎝ ⎜
⎞
⎠ ⎟−
1
2
a2 sin2ω
b2
⎛
⎝ ⎜
⎞
⎠ ⎟
⎡
⎣ ⎢
⎤
⎦ ⎥Sσ '
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−sinω −1
2cosω
⎛
⎝ ⎜
⎞
⎠ ⎟Sσ '
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S dσ 1,1exπ
( );S dσ 2 ,1eyπ
( )
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S dσ 1,2exπ
( );S dσ 2 ,2eyπ
( )
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S dπ1,a1π
( )
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S dπ 2 ,1exπ
( );S dπ 3 ,1eyπ
( )
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S dπ 2 ,2exπ
( );S dπ 3 ,2eyπ
( )
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cosθ1
2sin 2ω − 2cos2ω
⎛
⎝ ⎜
⎞
⎠ ⎟Sπ
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sinθ 2 cosω − 2sinω( )Sπ
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3 cosθ sin 2ω( )Sπ
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−cosθ sin 2ω + 2 cos2ω( )Sπ
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−sinθ 2cosω + 2 sinω( )Sπ
Symmetry Unique Metal-ligand Orbital Overlaps
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Sσ ' =3ab
a2 + b2Sσ
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sinθ =a2 sin 2ω + b2
a2 + b2
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cosθ =a cosω
a2 + b2 , , .
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* Only p-orbitals on the N atoms are considered
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-1.976 S-2.002 S
-0.892 S-0.816 S
1.590 S1.632 S
0.110 S0
-0.138 S0
-type
0.059 S0
-0.064 S0
-0.034 S0
1.058 S1.061 S
0.610 S0.612 S
-type
Case II (D3)Case I (Oh)Overlaps
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S dσ 1,1exσ
( );S dσ 2 ,1eyσ
( )
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S dσ 1,2exσ
( );S dσ 2 ,2eyσ
( )
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S dπ 2 ,1exσ
( );S dπ 3 ,1eyσ
( )
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S dπ 2 ,2exσ
( );S dπ 3 ,2eyσ
( )
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S dσ 1,2exπ
( );S dσ 2 ,2eyπ
( )
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S dπ 2 ,1exπ
( );S dπ 3 ,1eyπ
( )
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S dπ 2 ,2exπ
( );S dπ 3 ,2eyπ
( ) -1.976 S-2.002 S
-0.892 S-0.816 S
1.590 S1.632 S
0.110 S0
-0.138 S0
-type
0.059 S0
-0.064 S0
-0.034 S0
1.058 S1.061 S
0.610 S0.612 S
-type
Case II (D3)Case I (Oh)Overlaps
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S dσ 1,2exσ
( );S dσ 2 ,2eyσ
( )
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S dπ1,a1σ
( )
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S dπ 2 ,1exσ
( );S dπ 3 ,1eyσ
( )
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S dπ 2 ,2exσ
( );S dπ 3 ,2eyσ
( )
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S dσ 1,2exπ
( );S dσ 2 ,2eyπ
( )
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S dπ1,a1π
( )
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S dπ 2 ,1exπ
( );S dπ 3 ,1eyπ
( )
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S dπ 2 ,2exπ
( );S dπ 3 ,2eyπ
( )
Case I: Oh
Case II: D3
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S(dσ 1,1exπ );S(dσ 2,1ey
π )
1515
CD spectra- acac
d-to-d, LMCT as well as MLCT and LC, etc.
Global red-shift applied to the computed excitation energies:Cr(III): –5.0 103 cm–1
Co(III): –4.0 103 cm–1
theor. expt.
HC
O
H3C
-O
CH3
acac
- thiox
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-S
OO
S-thiox
1717
a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ = 0 for ideal octahedrons. c Trigonal splitting of the T1g state. d Polar distortion; s/h = 1.22 for ideal octahedrons.
σ-bonded
Early rule proposed for Λ-configuration:Azimuthal contraction ( < 0) positive R(E)Polar compression (s/h > 1.22) (E) < (A2)
Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L)3]n+
s
h
φ
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Rotatory strengths R ( ) and overlaps S(d2, ) ( ) against xe1
S
R /
10-4
0 cgs
/ degree
S / S
-80
-60
-40
-20
0
20
40
30 35 40 45 50 55-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
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R(1A21 )
R(1E1)
R(2E1) (1A2)
(2E)(1E)
b
€
aM
N
N
N
N
N
N
191919
a Sign of rotatory strength of the E symmetry. b Azimuthal distortion; Δ = 0 for ideal octahedrons. c Trigonal splitting of the T1g state. d Polar distortion; s/h = 1.22 for ideal octahedrons.
Relationship between CD of the d-d transitions and geometry in Λ-[M(L-L)3]n+
φ
s
h
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Complexes with Conjugated Ligands (Trigonal Dihedral)
N
M
N
N
N
N
N
M: Fe, Ru, OsN-N: bpy, phen
[Λ-Os(bpy)3]2+
E
A2
Exciton CD (LC π-π* transitions )
For the Λ configuration: R(E) > 0, R(A2) < 0, υ(A2−E) > 0
theor.expt.
5
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απ
βπ
22
N
N
N
N
zx
N
N
y N
N
N
N
NN
y'
x'
L1
L2
L3M
y'
x'
NN
short axis
long axis
x'
z'
y'
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α μy' β π = 2.397, β π lx' α π = −0.2394 R(A2) < 0 and R(E) > 0 for 0 < < 90
(απ−>βπ)
Energy Splitting of CD Bandsd-to-d: trigonal splitting of dπ orbitals due to
metal-ligand interactions
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[Co(en)3]3+
[Cr(en)3]3+
• d-Lσ E
A2
E
A2
polar compression (s/h > 1.22) (E) < (A2)
Co(acac)3
and Cr(acac)3
• d-Lπ/σE
A2
polar elongation(s/h < 1.22) (E) > (A2)
• LC: trigonal splitting of dπ orbitals due to metal-ligand interactions and electron-electron repulsion energy involving different number of ligands
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€
Eexciton = E(A2 ) − E(Ea ) = E(A2 ) − E(Eb ) = 3κ = 3 π I (1)∫ π I*(1)
1
r12
π II (2)π II* (2)dv1dv2
2525
/-bonded: d-to-d (might be safe), CT (not safe)
Determination of Absolute Configuration by CD
-bonded: d-to-d, LMCT ✔
/-bonded (conjugated ligands): LC exciton excitations ✔
Complexes with Tripodal Tetradentate Ligands (Trigonal bipyramidal)
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N NM
N
H3C H
NX
N NM
N
H3C H
NX
N NM
N
H3C H
NX
MeTPA MeBQPA MeTQA
Cu Cu Cu